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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Summer 2017 • Question 3

Question

Math 6210 • Real Analysis Summer 2017 • Question 3

Prove that for every Hilbert space, the set of isometries is closed in the strong operator topology. Show that there exist Hilbert spaces where the set of isometries is not closed in the weak operator topology.

Raw LaTeX

Prove that for every Hilbert space, the set of isometries is
closed in the strong operator topology. Show that there exist Hilbert spaces
where the set of isometries is not closed in the weak operator topology.

Topic Tags

Hilbert Spaces and Orthogonality Weak Topologies and Weak Convergence